Queueing Theory- Waiting Line Model, Heizer and Render
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The document discusses various queuing models, including single-channel and multichannel systems, and their application in real-world scenarios. It provides examples like a repairman at a shop serving customers and a recycling corporation analyzing the costs related to truck unloading times. The analysis considers factors such as arrival rates, service times, and associated costs to evaluate the efficiency of the queuing systems.
Queueing Theory- Waiting Line Model, Heizer and Render
- 26. Waiting-line System arrivals size limited unlimited pattern behavior waiting line limited unlimited queue discipline service queuing system design single-channel multiple- channel single-phase multiphase service time distribution constant negative exponential
- 27. Queuing Cost The three queuing models here all assume: • Poisson distribution arrivals • FIFO discipline • A single-service phase
- 28. Model Name Example A Single-channel Information counter system at department store (M/M/1) Number Number Arrival Service of of Rate Time Population Queue Channels Phases Pattern Pattern Size Discipline Single Single Poisson Exponential Unlimited FIFO
- 29. Model Name Example B Multichannel Airline ticket (M/M/S) counter Number Number Arrival Service of of Rate Time Population Queue Channels Phases Pattern Pattern Size Discipline Multi- Single Poisson Exponential Unlimited FIFO channel
- 30. Model Name Example C Constant- Automated car service wash (M/D/1) Number Number Arrival Service of of Rate Time Population Queue Channels Phases Pattern Pattern Size Discipline Single Single Poisson Constant Unlimited FIFO
- 31. Model Name Example D Limited Shop with only a population dozen machines (finite population) that might break Number Number Arrival Service of of Rate Time Population Queue Channels Phases Pattern Pattern Size Discipline Single Single Poisson Exponential Limited FIFO
- 32. Model A – Single-Channel (M/M/1
- 34. Sonnylye Lai, a repairman, at the SuicidalAccountant Shop, is able to install new keypad on calculators at an average rate of 3 per hour (or about 1 every 20 minutes). Customers seeking this service arrive at the shop on the average of 2 per hours, following a Poisson distribution. They are served on a first-in, first-out basis and come from a very large (almost infinite) population of possible buyers.
- 35. Sonnylye Lai, a repairman, at the SuicidalAccountant Shop, is able to install new keypad on calculators at an average rate of 3 per hour (or about 1 every 20 minutes). Customers seeking this service arrive at the shop on the average of 2 per hours, following a Poisson distribution. They are served on a first-in, first-out basis and come from a very large (almost infinite) population of possible buyers.
- 36. The owner of the SuicidalAccountant Shop estimates that the cost of customer waiting time, in terms of customer dissatisfaction and lost goodwill, is $10 per hour of time spent waiting in line. The average calculator has a 2/3-hour wait (Wq). There are approximately 16 calculator serviced per day (2 arrivals per hour times 8 working hours per day). The only other major cost that the owner can identify in the queuing situation is the salary of Sonnylyne, the repairman, who earns $7 per hour, or $56 per day. What is the total expected costs?
- 37. Model B – Multichannel (M/M/S)
- 41. Jeremy Corporation, collects and compacts aluminum cans and glass bottles in New York City. Its truck drivers currently wait an average of 15 minutes before emptying their loads for recycling. The cost of driver and truck time while they are in queues is valued at $60 per hour. A new automated compactor can be purchased to process truckloads at a constant rate of 12 trucks per hour (that is, 5 minutes per truck). Trucks arrive according to a Poisson distribution at an average rate of 8 per hour. If the new compactor is put in use, the cost will be amortized at a rate of $3 per truck unloaded. Evaluate the costs versus benefits of the purchase.